1. Introduction
- This article describes how to plot a correlogram.
- Correlogram is a graph of correlation matrix.
- It is very useful to highlight the most correlated variables in a data table.
- In this plot, correlation coefficients is colored according to the value.
- Correlation matrix can be also reordered according to the degree of association between variables.
- The R
{corrplot} package is used here.
2. Install R {corrplot} package
{corrplot} package is required to execute the R code in this article.
#install.packages("corrplot", quiet = TRUE)
3. Data for correlation analysis
- The
mtcars{datasets} data is used to compute correlation matrix.
library(dplyr, quietly = TRUE)
( res <- sample_n(tbl = mtcars, size = 10, replace = FALSE) )
## mpg cyl disp hp drat wt qsec vs am gear carb
## 1 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
## 2 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
## 3 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2
## 4 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
## 5 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
## 6 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
## 7 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
## 8 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
## 9 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
## 10 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
library(knitr, quietly = TRUE)
kable(x = res, caption = 'The random sampling of mtcars data set')
The random sampling of mtcars data set
| 13.3 |
8 |
350.0 |
245 |
3.73 |
3.840 |
15.41 |
0 |
0 |
3 |
4 |
| 33.9 |
4 |
71.1 |
65 |
4.22 |
1.835 |
19.90 |
1 |
1 |
4 |
1 |
| 21.4 |
4 |
121.0 |
109 |
4.11 |
2.780 |
18.60 |
1 |
1 |
4 |
2 |
| 15.8 |
8 |
351.0 |
264 |
4.22 |
3.170 |
14.50 |
0 |
1 |
5 |
4 |
| 24.4 |
4 |
146.7 |
62 |
3.69 |
3.190 |
20.00 |
1 |
0 |
4 |
2 |
| 14.3 |
8 |
360.0 |
245 |
3.21 |
3.570 |
15.84 |
0 |
0 |
3 |
4 |
| 19.2 |
6 |
167.6 |
123 |
3.92 |
3.440 |
18.30 |
1 |
0 |
4 |
4 |
| 21.0 |
6 |
160.0 |
110 |
3.90 |
2.875 |
17.02 |
0 |
1 |
4 |
4 |
| 19.7 |
6 |
145.0 |
175 |
3.62 |
2.770 |
15.50 |
0 |
1 |
5 |
6 |
| 16.4 |
8 |
275.8 |
180 |
3.07 |
4.070 |
17.40 |
0 |
0 |
3 |
3 |
4. Computing correlation matrix
( M <- cor( mtcars ) )
## mpg cyl disp hp drat wt
## mpg 1.0000000 -0.8521620 -0.8475514 -0.7761684 0.68117191 -0.8676594
## cyl -0.8521620 1.0000000 0.9020329 0.8324475 -0.69993811 0.7824958
## disp -0.8475514 0.9020329 1.0000000 0.7909486 -0.71021393 0.8879799
## hp -0.7761684 0.8324475 0.7909486 1.0000000 -0.44875912 0.6587479
## drat 0.6811719 -0.6999381 -0.7102139 -0.4487591 1.00000000 -0.7124406
## wt -0.8676594 0.7824958 0.8879799 0.6587479 -0.71244065 1.0000000
## qsec 0.4186840 -0.5912421 -0.4336979 -0.7082234 0.09120476 -0.1747159
## vs 0.6640389 -0.8108118 -0.7104159 -0.7230967 0.44027846 -0.5549157
## am 0.5998324 -0.5226070 -0.5912270 -0.2432043 0.71271113 -0.6924953
## gear 0.4802848 -0.4926866 -0.5555692 -0.1257043 0.69961013 -0.5832870
## carb -0.5509251 0.5269883 0.3949769 0.7498125 -0.09078980 0.4276059
## qsec vs am gear carb
## mpg 0.41868403 0.6640389 0.59983243 0.4802848 -0.55092507
## cyl -0.59124207 -0.8108118 -0.52260705 -0.4926866 0.52698829
## disp -0.43369788 -0.7104159 -0.59122704 -0.5555692 0.39497686
## hp -0.70822339 -0.7230967 -0.24320426 -0.1257043 0.74981247
## drat 0.09120476 0.4402785 0.71271113 0.6996101 -0.09078980
## wt -0.17471588 -0.5549157 -0.69249526 -0.5832870 0.42760594
## qsec 1.00000000 0.7445354 -0.22986086 -0.2126822 -0.65624923
## vs 0.74453544 1.0000000 0.16834512 0.2060233 -0.56960714
## am -0.22986086 0.1683451 1.00000000 0.7940588 0.05753435
## gear -0.21268223 0.2060233 0.79405876 1.0000000 0.27407284
## carb -0.65624923 -0.5696071 0.05753435 0.2740728 1.00000000
round(M, 2)
## mpg cyl disp hp drat wt qsec vs am gear carb
## mpg 1.00 -0.85 -0.85 -0.78 0.68 -0.87 0.42 0.66 0.60 0.48 -0.55
## cyl -0.85 1.00 0.90 0.83 -0.70 0.78 -0.59 -0.81 -0.52 -0.49 0.53
## disp -0.85 0.90 1.00 0.79 -0.71 0.89 -0.43 -0.71 -0.59 -0.56 0.39
## hp -0.78 0.83 0.79 1.00 -0.45 0.66 -0.71 -0.72 -0.24 -0.13 0.75
## drat 0.68 -0.70 -0.71 -0.45 1.00 -0.71 0.09 0.44 0.71 0.70 -0.09
## wt -0.87 0.78 0.89 0.66 -0.71 1.00 -0.17 -0.55 -0.69 -0.58 0.43
## qsec 0.42 -0.59 -0.43 -0.71 0.09 -0.17 1.00 0.74 -0.23 -0.21 -0.66
## vs 0.66 -0.81 -0.71 -0.72 0.44 -0.55 0.74 1.00 0.17 0.21 -0.57
## am 0.60 -0.52 -0.59 -0.24 0.71 -0.69 -0.23 0.17 1.00 0.79 0.06
## gear 0.48 -0.49 -0.56 -0.13 0.70 -0.58 -0.21 0.21 0.79 1.00 0.27
## carb -0.55 0.53 0.39 0.75 -0.09 0.43 -0.66 -0.57 0.06 0.27 1.00
5. Correlogram : Visualizing the correlation matrix
- R
corrplot{corrplot} function is used to plot the graph of the correlation matrix.
- The simplified format of the function is :
corr : The correlation matrix to visualize.
To visualize a general matrix, please use is.corr=FALSEmethod : The visualization method : circle, color, number, etc
library(corrplot, quietly = TRUE)
corrplot(M, method="circle")
6. Visualization methods
- Seven different visualization methods can be used:
circlesquareellipsenumbershadecolorpie
library(corrplot, quietly = TRUE)
corrplot(M, method="circle")
corrplot(M, method="square")
corrplot(M, method="ellipse")
# corrplot(M, method="number")
corrplot(M, method="shade")
corrplot(M, method="color")
corrplot(M, method="pie")
- Positive correlations are displayed in blue and negative correlations in red color.
- Color intensity and the size of the circle are proportional to the correlation coefficients.
- Display the correlation coefficient :
corrplot(M, method="number")
7. Types of correlogram layout
- There are three types of layout :
full (default) : display full correlation matrixupper : display upper triangular of the correlation matrixlower : display lower triangular of the correlation matrix
corrplot(M, type="upper")
corrplot(M, type="lower")
8. Reordering the correlation matrix
- The correlation matrix can be reordered according to the correlation coefficient.
- This is important to identify the hidden structure and pattern in the matrix.
hclust for hierarchical clustering order is used in the following examples.
# correlogram with "hclust" reordering
corrplot(M, type="upper", order="hclust")
# Using different color spectrum
col<- colorRampPalette(c("red", "white", "blue"))(20)
corrplot(M, type="upper", order="hclust", col=col)
# Change background color to lightblue
corrplot(M, type="upper", order="hclust", col=c("black", "white"), bg="lightblue")
9. Changing the color of the correlogram
- As shown in the above section, the color of the
correlogram can be customized.
RcolorBrewer palette of colors are used in the R script below :
library(RColorBrewer, quietly = TRUE)
# brewer.pal{RColorBrewer} : ColorBrewer palettes
# Creates nice looking color palettes especially for thematic maps
corrplot(M, type="upper", order="hclust", col=brewer.pal(n=8, name="RdBu" ))
corrplot(M, type="upper", order="hclust", col=brewer.pal(n=8, name="RdYlBu"))
corrplot(M, type="upper", order="hclust", col=brewer.pal(n=8, name="PuOr"))
10. Changing the color and the rotation of text labels
tl.col (for text label color) and tl.srt (for text label string rotation) are used to change text colors and rotations.
corrplot(M, type="upper", order="hclust", tl.col="blue", tl.srt=45)
11. Combining correlogram with the significance test
- Computing the p-value of correlations
- To compute the matrix of p-value, a custom R function is used :
# mat : is a matrix of data
# ... : further arguments to pass to the native R cor.test{stats} function
cor.mtest <- function(mat, ...) {
mat <- as.matrix(mat)
n <- ncol(mat)
p.mat<- matrix(NA, n, n)
diag(p.mat) <- 0
for (i in 1:(n - 1)) {
for (j in (i + 1):n) {
tmp <- cor.test(mat[, i], mat[, j], ...)
p.mat[i, j] <- p.mat[j, i] <- tmp$p.value
}
}
colnames(p.mat) <- rownames(p.mat) <- colnames(mat)
p.mat
} # end function
# matrix of the p-value of the correlation
p.mat <- cor.mtest(mtcars)
head(p.mat[, 1:5])
## mpg cyl disp
## mpg 0.0000000000000000 0.000000000611268714 0.000000000938032654
## cyl 0.0000000006112687 0.000000000000000000 0.000000000001802838
## disp 0.0000000009380327 0.000000000001802838 0.000000000000000000
## hp 0.0000001787835254 0.000000003477860669 0.000000071426786557
## drat 0.0000177623992875 0.000008244636190317 0.000005282021688157
## wt 0.0000000001293959 0.000000121756701354 0.000000000012223195
## hp drat
## mpg 0.000000178783525 0.000017762399
## cyl 0.000000003477861 0.000008244636
## disp 0.000000071426787 0.000005282022
## hp 0.000000000000000 0.009988771894
## drat 0.009988771893526 0.000000000000
## wt 0.000041458274411 0.000004784260
- Add significance level to the
correlogram
- In the below figure,
- correlations with p-value > 0.01 are considered as insignificant.
- In this case, the correlation coefficient values are leaved blank or crosses are added.
# Specialized the insignificant value according to the significant level
corrplot(M, type="upper", order="hclust", p.mat = p.mat, sig.level = 0.01)
# Leave blank on no significant coefficient
corrplot(M, type="upper", order="hclust", p.mat = p.mat, sig.level = 0.01, insig = "blank")
12. Customize the correlogram
col <- colorRampPalette(c("#BB4444", "#EE9988", "#FFFFFF", "#77AADD", "#4477AA"))
corrplot(
M,
method="color",
col=col(200),
type="upper",
order="hclust",
# Add coefficient of correlation
addCoef.col = "black",
#Text label color and rotation
tl.col="red",
tl.srt=45,
# Combine with significance
p.mat = p.mat,
sig.level = 0.01,
insig = "blank",
# hide correlation coefficient on the principal diagonal
diag=FALSE
)
13. Conclusions
- Use
corrplot{corrplot} function to plot an elegant graph of a correlation matrix.